US7887234B2 - Maximum blade surface temperature estimation for advanced stationary gas turbines in near-infrared (with reflection) - Google Patents

Methods for maximum scene surface temperature estimation for blades with reflective surface properties in advanced stationary gas turbines are disclosed. The approach utilizes high speed infrared imagery provided by an online monitor system using a focal plan array (FPA) for near-infrared monitoring during engine runtime up to base load. The one waveband method for temperature estimation is assumed as starting point. A lower surface emissivity and higher surface reflectance of thermal barrier coating (TBC) in near-infrared can cause systematic estimation errors. Methods using the one wave band method, with the purpose to reduce estimation errors for maximum temperatures are also disclosed. Theoretical results, data from numerical simulations, and real data from engine test are provided. A system for performing temperature estimation methods is also disclosed.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No. 60/853,484, filed Oct. 20, 2006, which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to surface temperature estimation for blades with reflective surface properties in advanced stationary gas turbines. More specifically it relates to one waveband temperature estimation by high speed imagery for near-infrared radiation.

High speed infrared imagery provided by an online monitor system using a focal plan array (FPA) for near-infrared monitoring can be used during engine runtime up to base load for temperature estimation of turbine blades with reflective surface properties. The one waveband method for temperature estimation may be assumed as starting point. However, a lower surface emissivity and higher surface reflectance of thermal barrier coatings (TBC) in near-infrared can cause systematic estimation errors.

Accordingly, new and improved one waveband near-infrared imagery related methods and systems are required for temperature estimation that will reduce estimation errors.

SUMMARY OF THE INVENTION

The present invention provides improved temperature estimation for gas turbines and other bodies.

In accordance with one aspect of the present invention, a method for one waveband maximum scene temperature estimation from radiated heat from a surface of a body by a radiation sensor, comprising: receiving an image with the sensor; creating a non-uniformity corrected (NUC) image having a plurality of pixels from the image, a pixel having a pixel value; creating a direct one waveband temperature inverse calibration correspondence related to reflected radiation; and transforming the pixel value into an estimated temperature value by using the direct one wave band temperature inverse calibration correspondence.

In accordance with further aspects of the present invention, the method also includes performing a false color transformation.

In accordance with another aspect of the present invention the body can be a part the hot gas path of a gas turbine with reflective surface properties.

In accordance with further aspects of the present invention, observed radiation by the sensor can be expressed by:

E = ∫ λ = 900 ⁢ ⁢ nm λ = 1700 ⁢ ⁢ nm ⁢ S ⁡ ( λ ) ⁢ ɛ ⁡ ( λ ) ⁢ B ⁡ ( T , λ ) ⁢ ⅆ λ + ∫ λ = 900 ⁢ ⁢ nm λ = 1700 ⁢ ⁢ nm ⁢ S ⁡ ( λ ) ⁢ ( 1 - ɛ ⁡ ( λ ) ) ⁢ g ⁢ ⁢ ɛ ⁡ ( λ ) 1 - g ⁡ ( 1 - ɛ ⁡ ( λ ) ) ⁢ B ⁡ ( T 0 , λ ) ⁢ ⅆ λ .

In accordance with another aspect of the present invention the waveband of wavelengths λ1 to λ2 can be within the waveband of infrared radiation.

In accordance with further aspects of the present invention, λ1 is essentially 900 nm and λ2 is essentially 1700 nm.

In accordance with further aspects of the present invention, the method comprises deriving the inverse calibration correspondence by representing an estimated temperature as a function of a pixel value.

In accordance with another aspect of the present invention, the inverse calibration correspondence for temperature estimation is based on a grey body radiation model with ε<1.

In accordance with further aspects of the present invention, the inverse calibration correspondence is corrected for an applied radiation model.

In accordance with another aspect of the present invention, the pixel value is determined by a first term summed with a corrective term depending from reflective radiation.

The present invention also provides a system that performs steps including the steps just described. The system can include: an infrared imagery monitor system that can provide images, a processor, and software operable on the processor to perform the previously described steps.

DESCRIPTION OF THE DRAWINGS DESCRIPTION OF A PREFERRED EMBODIMENT

Several factors such as surface reflection, absorption, gas emittance, lens attenuation, lens shading, sensor drift, numerical approximations or other effects can have an impact on the accuracy of the temperature estimation. Systematic temperature estimation errors can be expected, if for example emissivity changes or reflected radiation are not taken into account. Relevant for blade surface temperature estimation are two surface materials thermal barrier coating (TBC) and base material. It is known that the emissivity, reflectance and transmittance of TBC can change as a function of wavelength, temperature and age. Uncoated blades have different surface properties than coated blades. It is possible, that surface properties can also change due to deposits on the blade.

The radiated power from the blade is in general a mixture of emitted, reflected and transmitted components. Hot gasses between the blade surface and the lens tube can absorb and emit radiation. Water condensation or deposits on the lens surface, lens shading or limited lens collection, absorption, reflection, or optical filters will cause signal loss and eventually scatter radiation. The InGaAs focal plane array has a specific spectral sensitivity in the near infrared domain from 0.9 μm to 1.6 μm and can collect radiant power within this range. The electric signal generated from the collected charge at each sensor element is also a function of camera parameter. The signal can be distorted by sensor noise and spatial non-uniformities.

Summary of some effects which may compromise temperature estimation:

• • Uncertainty of target emissivity (due to deposits, aging, sensitive to temperature and wavelength)
  • Reflected radiation from surrounding
  • Transmitted radiation from bond coat
  • Emission or absorption form sight hot gas path
  • Deposits on lens surface
  • Lens shading
  • Sensor sensitivity and sensor noise at 1-3 μs integration time
    Direct One Wave Band Blade Surface Temperature Estimation

The direct one wave band blade surface temperature estimation method is based on the relationship between blade surface temperature and emitted radiant power as described by the Planck law.

• Planck(λ)—Spectral radiant emittance, W cm⁻² mu⁻¹
• λ—Wavelength
• c₁=2πhc₂=3.7414E4—First radiation constant
• c₂=ch/k=1.43879E4—Second radiation constant
• T—Absolute material temperature in K
• ε_λ—Spectral material emissivity

It is assumed, that the thermal emitted radiant power is a function of the surface temperature T and surface emissivity ε. A lens aimed at the target from distance d with a spectral transfer characteristic Lens(λ, d) collects and projects radiation from the target onto the FPA sensor array. Each sensor element on the array can accumulate incident radiation depending on the sensor spectral sensitivity Sensor(λ) for a given integration time Δt. The accumulated charge at each sensor element is then amplified and converted to a digital representation described by the camera response function Cam( ).

PixelValue = Cam ⁡ ( ∫ + Δ ⁢ ⁢ t ⁢ ∫ λ = 900 ⁢ ⁢ nm λ = 1700 ⁢ ⁢ nm ⁢ Sensor ⁡ ( λ ) ⁢ Lens ⁡ ( λ , d ) ⁢ Planck ⁡ ( T , λ ) ⁢ ɛ ⁢ ⅆ λ ⁢ ⅆ t ) ( 2 ⁢ - ⁢ 2 )

The direct one waveband temperature estimation method assumes that the relationship between surface temperature T and sensor PixelValue, equation (2-2) can be recorded experimentally and inverted. In praxis the temperature estimation sensor system is calibrated prior to the test by recording the relationship between TBC surface temperature and observed pixel count value from the sensor using a TBC sample in an oven with controlled temperature. It is important that the calibration setup, setup geometry, the lens system, camera settings and filters are in principal identical to the test setup.

It is assumed in this process that the hardware setup between calibration and test are in principal identical and the target emissivity does not change over time. Signal distortions due to additional reflected or transmitted signals are not explicit taken into account. It is important that sensor parameters remain identical between calibration and measurement.

The relationship between surface temperature and pixel response values is recorded in two transformations. The first transformation is a sensor specific non-uniformity correction (NUC). The purpose of the NUC is to reduce variations between sensor elements (pixels). These variations can include pixel dependent non-uniformities caused by the sensor array or spatial non-uniform lens attenuation. The lens correction is for example one spatial non-uniform lens shading effect.

The NUC transformation requires and individual transformation for each sensor element on the FPA. Individual NUC functions for sensors elements (x,y) on the focal plain array (FPA) are represented by lower order polynomials:

N ⁢ ⁢ U ⁢ ⁢ C ⁡ ( x , y , I ⁡ ( x , y ) ) ≈ ∑ k = 0 n ⁢ b k ⁡ ( x , y ) ⁢ I k ⁡ ( x , y ) ( 2 ⁢ - ⁢ 3 )

T ⁡ ( I ) ≈ ∑ k = 0 m ⁢ c k ⁢ I k ( 2 ⁢ - ⁢ 4 )

The parameters c_k of the temperature estimation curve in equation (2-4) are estimated by minimizing the weighted mean square error, equation (2-5), between the measured calibration target temperature T and the observed non-uniformity corrected sensor response I, using n samples (i=1 . . . n).

Q = ∑ i = 1 ⁢ ⁢ … ⁢ ⁢ n ⁢ w i ⁡ ( T i - ∑ k = 0 m ⁢ c k ⁢ I i k ) 2 ( 2 ⁢ - ⁢ 5 )

Maximum Scene Temperature Estimation Using One Wave Band

The described maximum scene temperature estimation is derived from an upper temperature bound. Three different image formation models are considered: black body point source, gray body point source, gray body point source with reflection. Most realistic is the gray body model with reflection. The analysis shows how much a gray body point source model approximates the gray body point source model with reflection if maximum temperatures in the scene are of interest. The approximation errors for the gray body point source model and for the black body model are compared in detail. If the black body calibration curve in NIR is used for TBC blade temperature estimation, then maximum temperatures will be underestimated significantly by more then 100 Kelvin. Using a gray body calibration curve in NIR will systematically overestimate temperatures, but the estimation error decreases with higher scene maximum temperatures compared to the average environment temperature.

Upper Bound of Temperature Estimation

If B(T,λ) is the Planck law spectral radiance and S(s) the spectral sensitivity and collection of a sensor and lens as described in Richard D. Hudson, Jr. “Infrared System Engineering” John Wiley & Sons, New York, 1996, then the observed black body radiation (emissivity=1) in near-infrared is given by:

E Blackbody = ∫ λ = 900 ⁢ ⁢ nm λ = 1700 ⁢ ⁢ nm ⁢ S ⁡ ( λ ) ⁢ B ⁡ ( T , λ ) ⁢ ⅆ λ ( 3 ⁢ - ⁢ 1 )

The surface temperature (in equation 3-1) is described by T and the wavelength is denoted by λ. It is assumed in equation (3-1) and for the following argumentation, that the effect of the sensor viewing direction with respect to the surface normal can be ignored. This is a justified approximation for TBC, where the observed radiation is almost invariant to the viewing direction.

The observed radiation from a gray body point source, isolated from the environment, with a spectral surface emittance ε(λ) is given by:

The average scene radiance E₀ from an arbitrary surface patch can be approximated using the equilibrium, in which on average the surface radiance is equal to the mixture of the (gray body) thermal emittance εB₀ and the irradiance from the environment gE₀ multiplied with the surface reflectance r. The approximated average scene temperature is denoted by T₀.

Average patch signal in scene:
E ₀ =εB ₀ +grE ₀  (3-6)

E 0 = ɛ 1 - rg ⁢ B 0 ( 3 ⁢ - ⁢ 7 )

Replace reflectance r=1−ε,

E 0 = ɛ 1 - g ⁡ ( 1 - ɛ ) ⁢ B 0 ( 3 ⁢ - ⁢ 8 )

The incident radiation E₁(λ) is then given by:

E 1 ⁡ ( λ ) = gE 0 = g ⁢ ɛ ⁡ ( λ ) 1 - g ⁡ ( 1 - ɛ ⁡ ( λ ) ) ⁢ B ⁡ ( T 0 , λ ) ( 3 ⁢ - ⁢ 9 )

Equation (3-8) ignores material transmittance. Equation (3-6) requires a geometry factor g which is defined as the ratio of the area of the cavity that contributes to the irradiance (A_All−A_open) to the total surrounding area A_All.

g = A All - A open A All ( 3 ⁢ - ⁢ 10 )

The observed radiation from a patch described by equation (3-3) transforms with substitution from equation (3-9) into:

E = ∫ λ - 900 ⁢ ⁢ nm λ = 1700 ⁢ ⁢ nm ⁢ S ⁡ ( λ ) ⁢ ɛ ⁡ ( λ ) ⁢ B ⁡ ( T , λ ) ⁢ ⅆ λ + ⁢ ∫ λ = 900 ⁢ ⁢ nm λ = 1700 ⁢ ⁢ nm ⁢ S ⁡ ( λ ) ⁢ ( 1 - ɛ ⁡ ( λ ) ) ⁢ g ⁢ ⁢ ɛ ⁡ ( λ ) 1 - g ⁡ ( 1 - ɛ ⁡ ( λ ) ) ⁢ B ⁡ ( T 0 , λ ) ⁢ ⅆ λ ( 3 ⁢ - ⁢ 12 )

Equation (3-12) describes the observed radiation from a surface patch with temperature T and emissivity ε(λ) in an environment with an average scene temperature T₀ and emissivity of ε(λ), with an average effective visible surrounding area defined by the parameter g.

In case of uniform temperature T=T₀ equation (3-12) simplifies to the cavity

equation ⁢ : ⁢ ⁢ E = ∫ λ = 900 ⁢ ⁢ nm λ = 1700 ⁢ ⁢ nm ⁢ S ⁡ ( λ ) ⁢ ɛ ⁡ ( λ ) ⁢ ( 1 + g ⁡ ( 1 - ɛ ⁡ ( λ ) ) 1 - g ⁡ ( 1 - ɛ ⁡ ( λ ) ) ) ⁢ B ⁡ ( T 0 , λ ) ⁢ ⅆ λ ( 3 ⁢ - ⁢ 13 )

For a total enclosed environment (cavity) with uniform temperature (g=1) equation (3-13) reduces to a black body source with an effective emissivity of one as is shown in the following equation.

ɛ ⁡ ( λ ) ⁢ ( 1 + 1 ⁢ ( 1 - ɛ ⁡ ( λ ) 1 - 1 ⁢ ( 1 - ɛ ⁡ ( λ ) ) ) = ɛ ⁡ ( λ ) ⁢ ( 1 + 1 - ɛ ⁡ ( λ ) 1 - 1 + ɛ ⁡ ( λ ) ) = ɛ ⁡ ( λ ) + 1 - ɛ ⁡ ( λ ) = 1 ( 3 ⁢ - ⁢ 14 )

This is consistent with results for cavities published by Gouffe and described in Richard D. Hudson, Jr. “Infrared System Engineering” John Wiley & Sons, New York, 1996. An open environment, described by g=0, transforms equation (3-13) into a point source with emissivity ε(λ):

If the surface patch temperature is smaller then the average scene temperature T₀ (T<T₀), then the observed radiated power will converge to the average scene radiation defined by the average scene temperature. In this case, the right integral of equation (3-3) is then more dominant.

Table 1 compares the real surface temperature with the estimated temperature values using a black body calibration curve derived from equation (3-1) and a gray body point calibration curve equation (3-2). It can be seen that the estimated temperature from the black body calibration curve is underestimating the real surface temperature at higher temperatures significantly, by more than 100K. The upper temperature estimation bond provides a more accurate estimate for higher temperatures. For a particular case, where the maximum temperature is about 150K higher than the average scene temperature, the maximum estimated temperature using the direct (black body model) temperature estimation is 130 Kelvin lower. The gray body temperature estimation method overestimates the temperature in this case by only 35 Kelvin.

Results on Real Data

The sensor system was calibrated using a TBC sample in a brick oven with controlled temperature. The measured irradiance on the sensor is a mixture of thermal emittance from TBC surface ε(λ)P(T₀,λ) and reflected radiation form the brick surrounding (g(1−ε(λ))ε_brick(λ))P(T₀,λ). The measured irradiance on the sensor is then given by:

The recorded sensor calibration curve is based on an effective emissivity of 0.89 and can be converted to the corresponding TBC point source calibration curve with emissivity 0.35 as required for the maximum temperature estimation using a conversion factor p:

It is another aspect of the present invention to adjust a calibration curve of estimated temperatures derived from one waveband optical measurements by a factor that is dependent on a radiation model. It was demonstrated how the radiation model such as black body or grey body assumptions can create systematic estimation errors in a calibration curve. Accordingly it is an aspect of the present invention to correct estimated temperatures based on applied radiation models in creating calibration curves.

As an aspect of the present invention, and as was shown above, a temperature can be estimated by applying a calibration or an inverse calibration. As an illustrative example means for calibration are provided as a calibration curve. Means of calibration, as an aspect of the present invention, can be provided in different forms. For instance a means for calibration can be provided as a curve, as a table, as a formula, as a calibration factor, as a calibration correspondence or in any other form that is useful to apply calibration for estimating a temperature. A processor, in accordance with another aspect of the present invention, can use this calibration information in whatever form presented to determined temperatures and other information.

System

The following references are generally descriptive of the background of the present invention and are hereby incorporated herein by reference: [1] Technical report: TR-05178 at Siemens Power Generation, Orlando. [2] R. M. Haralick and L. G. Shapiro. Computer and robot vision, vol. 2, New York, Addison Wesley, 1993. [3] Richard D. Hudson, Jr. “Infrared System Engineering”, John Wiley & Sons, New York, 1996. [4] M. Voigt, M. Zarzycki, D. LeMieux, V. Ramesh, “Scene-based nonuniformity correction for focal plane arrays using a facet model”, Proceedings of the SPIE “Infrared Technology and Applications XXXI, Volume 5784, pp. 331-342 (2005). [5] T. Schulenberg, H. Bals, “Blade Temperature Measurement of Model V84.2 I00 MW/60 Hz Gas Turbine”, Gas Turbine Conference and Exhibition, Anaheim, Calif., May 31-Jun. 4, 1987, [6] J. Markham, H. Latvakoski, D. Marran, J. Neira, P. Kenny, P. Best “Challenges of Radiation Thermometry for Advanced Turbine Engines” Proceedings of the 46th International Instrumentation Symposium, ISA Volume 397, 2000 [7] Beynon, T. G. R., 1981, “Turbine Pyrometry An Equipment Manufacturer's View” SME 81-GT-136.

While there have been shown, described and pointed out fundamental novel features of the invention as applied to preferred embodiments thereof, it will be understood that various omissions and substitutions and changes in the form and details of the system and methods illustrated and in its operation may be made by those skilled in the art without departing from the spirit of the invention. It is the intention, therefore, to be limited only as indicated by the scope of the claims appended hereto.